When a string of sensors or string sensors are positioned in a magnetic field generated by a multi-pole magnet, the sensors generate sine and cosine signals due to the magnetic field. The sine and cosine signals can then be used to detect positional information of the sensors. Particularly, the sensors are first divided into a plurality of sections of sensors, and outputs of the sections of sensors are summed and subtracted from each other to form the sine and cosine signals.
The sine and cosine signals formed from the outputs of the sensors are affected by other processes and parameters. For example, amplitudes of the sine and cosine signals will be mismatched if lengths of the multi-pole magnet and the sensor string are improperly matched. Additionally, the amplitudes of the sine and cosine signals have to be matched before the sine and cosine signals are interpolated. Typically, the amplitudes of the sine and cosine signals are matched by attenuating or amplifying the outputs of the sections of sensors by a gain factor such that the amplitudes of the sine and cosine signals are equal or normalized.